A horizontal pipe with an I.D. = 10 cm and a length = 3000 cm is filled with sand. The sand packed in the tube has a porosity of 20%. The sand pack is filled to contain a water saturation of 30% and an oil saturation of 70%. At these saturations the water is immobile, that is, it does not flow when the system is subjected to a pressure difference. The oil will flow when subjected to a pressure drop and the permeability to oil is 200 md. The viscosity of the oil is 0.65 cp. If oil is now injected at a constant rate, calculate the following: a. What is the Darcy velocity (apparent velocity) of the oil if the pressure drop across the length of the pipe is 100 psi? b. What is the flow rate in cm3/sec? c. Calculate the volume of oil contained in the pipe initially and the time required to displace all of the initial oil out of the sand pack. d. From the time calculated in part c), calculate the actual average velocity in the sand pack (interstitial velocity). e. Calculate the interstitial velocity using the Darcy velocity, the porosity and the immobile water saturation.